A Pawn is as Strong as the Hand that Holds It -- Thought Experiment

Imagine a series of games played by a computer program that makes
random legal moves for both sides; imagine further that in every
game of the series, Black is giving Queen odds (has no Queen in the
starting position).

Even with random moves, White is going to win more than 50% of the
games. Who knows? White might even win 60% of the time!

Now imagine a series of games played between Kasparov and Karpov,
and in every game Black gives Queen odds. Do you think that Black
could even manage to draw one game in a thousand?

Evidently, stronger players need less of an advantage to force a
decisive result. (Duh. What a revelation!)

The converse should be true as well: if a pair of players plays a
series of games where they give each other Knight odds, the average
rating of those two players could theoretically be derived from the
winning percentage. In practice we do not have the data that would
tell us "if the odds-giver won one game in five, the average rating
of the two players is 1600", or something like that; but if we did,
it would be possible to give people (or new computers) fairly
accurate ratings without their having any exposure to the general
public of chessplayers.

And In Closing, May I Say

Because small differences are more significant to stronger players,
a game of Chess with Different Armies could be very equal for
masters and very unequal for grandmasters.